What is expand (x-y)/(i+y)*t ?

The solution to expand (x-y)/(i+y)*t is (-y^2t+xyt)/(1+y^2)+i(-xt+yt)/(1+y^2)

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expand (x-y)/(i+y)*t

expand

\frac{x - y}{i + y} \cdot t

\frac{- y ^{2} t + x y t}{1 + y ^{2}} + i \frac{- x t + y t}{1 + y ^{2}}

Solution steps

\frac{x - y}{i + y} t

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{( x - y ) t}{i + y}

Expand

(x - y) t : x t - y t

= \frac{x t - y t}{i + y}

Rationalize

\frac{x t - y t}{i + y} : \frac{( y - i ) ( x t - y t )}{y ^{2} + 1}

= \frac{( x t - y t ) ( y - i )}{y ^{2} + 1}

Rewrite

\frac{( x t - y t ) ( y - i )}{y ^{2} + 1}

in standard complex form:

\frac{x y t - y ^{2} t}{y ^{2} + 1} + \frac{- x t + y t}{y ^{2} + 1} i

= \frac{x y t - y ^{2} t}{y ^{2} + 1} + \frac{- x t + y t}{y ^{2} + 1} i

(x - 3) (sin (π x))

\frac{1}{( 1 - 6 t ) ^{4}}

\frac{d}{d x} ((c) (x - c)^{2})

x^{2} \frac{d}{d x} ((y) (y - x y))

(- d + e) (4 e + d)

What is expand (x-y)/(i+y)*t ?
The solution to expand (x-y)/(i+y)*t is (-y^2t+xyt)/(1+y^2)+i(-xt+yt)/(1+y^2)